Predictive Simulations in a Stochastic Environment
Predictive simulations, or trajectory optimizations, are generally solved by minimizing some objective while assuming no noise. However, previous studies show that noise is important in movement selection of humans. Therefore, we propose a novel approach to solve predictive simulations in a stochastic environment.
In this approach, many noisy episodes of one trajectory are solved, while each should have the same feedforward and feedback controller. So in gait, instead of one gait cycle, a predictive optimization would be performed over many gait cycles, while there is an open loop controller and a closed loop controller, the latter is a function of state.
We have shown that we can successfully use this method by predicting an optimal trajectory for a one degree of freedom pendulum swing-up in a noisy environment that is different from the optimal trajectory in a deterministic environment. This ‘stochastic trajectory’ swings up later to avoid spending time in the upward position, an unstable equilibrium.
We will also implement this method on predictive simulations of gait. First, on a torque controlled model, we aim to show that foot-ground clearance is larger in a noisy environment. Later, we will implement this method also on predictive simulation of gait of persons with a transtibial amputations. These simulations should predict co-contraction on the upper residual leg due to an imperfect connection with the prosthetic leg.
Anne Koelewijn: Trajectory Optimization in Stochastic Multibody Systems using Direct Collocation. Fourth International Conference on Multibody System Dynamics, Montreal, QC. (abstract)